How do I make objects translucent but keep background images solid?
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In Blender 2.8 and on, there is an option to enable translucency in a scene, called X-Ray. It can be found in the shading options in the viewport.



Once that is enabled, everything in the scene goes translucent. Images may also go translucent depending on how you imported them. If you import your reference by going Shift+A, >Image >Reference they will stay fully opaque.